" 5.(i) "x^(3)log_(e)x

Evaluate: int(e^(5)(log)_(e)x-e^(4)(log)_(e)x)/(e^(3)(log)_(e)x-e^(2)(log)_(e^(x))x)dx

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

The value of int(e^(5log_(e)x)+e^(4log_(e)x))/(e^(3log_(e)x)+e^(2log_(e)x))dx is

Evaluate: int(e^(5(log)_(e)x)-e^(4(log)_(e)x))/(e^(3(log)_(e)x-e^(2log x)))dx

Find the inverse of the following function.( i ) f(x)=sin^(-1)((x)/(3)),x in[-3,3]( ii )f(x)=5^(log_(e)x),x>0 (iii) f(x)=log_(e)(x+sqrt(x^(2)+1))

int(e^(6log_(e)x)-e^(5log_(e)x))/(e^(4log_(e)xe^(3log_(e)x))) backslash dx

The differentiation of log _(e)x,x>0is(1)/(x)* i.e.(d)/(dx)(log_(e)x)=(1)/(x)

Find the domain and range of following functions (i) f(x)=log_(e)(sinx) (ii) f(x)=log_(3)(5-4x-x^(2))